Related papers: The escape problem for mortal walkers
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
Interesting theoretical problems of target search or threshold crossing, formally known as {\it first passage}, often arise in both diffusive transport problems as well as problems of chemical reaction kinetics. We study three systems…
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small "escape window" in the otherwise impermeable boundary, once it arrives to this window and over-passes an…
Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models…
This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its…
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
We consider a walker moving in a one-dimensional interval with absorbing boundaries under the effect of Markovian resettings to the initial position. The walker's motion follows a random walk characterized by a general waiting time…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
We investigate the first-passage properties of bursty random walks on a finite one-dimensional interval of length L, in which unit-length steps to the left occur with probability close to one, while steps of length b to the right --…
It is now well established that microswimmers can be sorted or segregated fabricating suitable microfluidic devices or using external fields. A natural question is how these techniques can be employed for dividing swimmers of different…
The out-of-equilibrium character of active particles, responsible for accumulation at boundaries in confining domains, determines not-trivial effects when considering escape processes. Non-monotonous behavior of exit times with respect to…
We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided…
We obtain an exact formula for the first-passage time probability distribution for random walks on complex networks using inverse Laplace transform. We write the formula as the summation of finitely many terms with different frequencies…
We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability $r$. We construct a discrete renewal…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is…
Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Typical mathematical treatments are based on formulations that…
Suppose we are given the free product $V$ of a finite family of finite or countable sets $(V_i)_{i\in\mathcal{I}}$ and probability measures on each $V_i$, which govern random walks on it. We consider a transient random walk on the free…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We study the transition probability, say $p_A^n(x,y)$, of a one-dimensional random walk on the integer lattice killed when entering into a non-empty finite set $A$. The random walk is assumed to be irreducible and have zero mean and a…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…